I see. I meant 'energetically accessible', but you mean more like 'affordably accessible' (in the sense that the molecular toolkit of a cell is what can 'afford' certain structures, due to chaperones available and so on).
Who knows what might be possible if you designed a cell from scratch - perhaps you could rework all the machinery to access other parts of fold space. After all, there are some weird and wonderful machines out there like the 'Vault' (https://en.wikipedia.org/wiki/Vault_(organelle)) that can fit whole proteins inside them. Possibly a different cage-like structure could help fold designed proteins into as-before unseen structures.
It could also mean "evolutionarily accessible". The basin of attraction in sequence space has to be sufficiently large that evolution could stumble across it.
Who knows what might be possible if you designed a cell from scratch - perhaps you could rework all the machinery to access other parts of fold space. After all, there are some weird and wonderful machines out there like the 'Vault' (https://en.wikipedia.org/wiki/Vault_(organelle)) that can fit whole proteins inside them. Possibly a different cage-like structure could help fold designed proteins into as-before unseen structures.